Chapter SH, Problem 7.19EP

To determine

To find:the solution of the equation and round off the solution to near ten-thousand.

Answer to Problem 7.19EP

  $\text{x=2}\text{.5541}$ .

Explanation of Solution

Given:

  ${\text{5}}^{\text{x}}\text{=60}$ .

Concept used:

According the logarithmic formula:

  ${\text{logx}}^{\text{a}}=\text{alogx}$ .

Value of the logarithm can be calculated through calculator or logarithmic table.

Calculation:

Here the given equation:

  ${\text{5}}^{\text{x}}\text{=60}$ .

Multiplying both side $\text{log}$ operator:

  ${\text{log5}}^{\text{x}}\text{=log60}$ .

According the logarithmic formula:

  ${\text{logx}}^{\text{a}}=\text{alogx}$ .

So, the given equation ${\text{log5}}^{\text{x}}\text{=log60}$ can be written as:

  $\text{xlog5=1}\text{.778}$ .

  $\text{x}\left(0.6989\right)\text{=1}\text{.7781}$ .

  $\text{x=2}\text{.5541}$ .